• 한국안전학회지
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• 제22권4호
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• pp.13-19
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• 2007

An numerical method to estimate thermal diffusivity has been developed for one-dimensional unsteady heat conduction problem, when the temperatures are know at two positions in a semi-infinite body. Using the closed form solution which has already derived an explicit solution for the inverse problem for one-dimensional transient heat conduction using Laplace transform technique, we first estimate the surface temperature. The thermal diffusivity can be estimated by using the estimated surface temperature and measured temperatures, which include some uncertainties. The estimated surface heat flux and thermal diffusivity are found to be in good agreement with those of the experimented conditions. This method will be extended to the simultaneous measurement of thermal diffusivity and thermal conductivity.

• Steel and Composite Structures
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• 제48권6호
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• pp.641-648
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• 2023

In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.

• 한국경영과학회지
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• 제15권1호
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• pp.99-115
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• 1990

This paper is concerned with the unit commitment problem in an electric power system with both thermal and pumped-storage hydroelectric units. This is a mixed integer programming problem and the Lagrangean relaxation method is used. We show that the relaxed problem decomposes into two kinds of subproblems : a shortest-path problem for each thermal unit and a minimum cost flow problem for each pumped-storage hydroelectric unit. A method of obtaining an incumbenet solution from the solution of a relaxed problem is presented. The Lagrangean multipliers are updated using both subgradient and incremental cost. The algorithm is applied to a real Korean power generation system and its computational results are reported and compaired with other works.

• 대한기계학회논문집A
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• 제30권8호
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• pp.949-956
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• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

• 한국항공운항학회지
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• 제16권4호
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• pp.26-34
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• 2008

This article provides a comprehensive treatment of cracks in non-homogeneous structural materials such as functionally graded materials (FGMs). It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using laminated composite plate model to simulate the material non-homogeneity, we present an algorithm for solving the system based on Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. As a numerical illustration, transient thermal flow intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of non-homogeneous material with properties varying in the thickness direction.

• 한국전기전자재료학회논문지
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• 제28권3호
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• pp.208-212
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• 2015

This study will design the structural optimization of 21 W LED heat sink using the thermal conductive plastic materials. The thermal conductive plastic heat sink is inferior to aluminum heat sinks in thermal properties. This study will solve this problem using formability of thermal conductive plastic heat sink. A heat sink was optimized in terms of the number, and the thickness of fins and the base thickness of the heat sink, using the Heatsinkdesigner software. Also by using SolidWorks Flow simulation and thermal analysis software, the thermal characteristics of the heat sink were analyzed. As the result, the optimized heat sink has 17 fins, which are 1.5 mm thick and a 3.7 mm-thick base. The highest and the lowest temperature were $51.65^{\circ}C$ and $46.24^{\circ}C$ respectively. Based on these results, The thermal conductive plastic heat sink is considered possible to overcome heating problem when designing in complex structure.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.75-82
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• 2005

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as $0\;{\leq}\;r\;{\leq}\;a,\;0\;{\leq}\;z\;{\leq}\;h$. The results, obtained in the series form in terms of Bessel's functions, are illustrated numerically.

• 대한기계학회논문집A
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• 제21권1호
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• pp.133-143
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• 1997

Piezoelastic materials have recently attracted considerable attention because of their potential use in intelligent structural systems. In this paper, we treat a transient piezothermoelastic problem in a hexagonal plate of crystal class 6mm subjected to antisymmetric heating temperature. We analyze this problem by use of the potential function method. Numerical calculations are carried out for a cadmium selenide solid, and the results are presented graphically in comparison with those derived from the similar problem in a cadmium selenide plate subjected to symmetric heating temperature for a symmetry transient problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권2호
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• pp.73-86
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• 2009

The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using the variational method technique. The problem is characterized by two parameters: the Nusselt number(N) and the dynamic parameter($\Lambda$). We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.